-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '967279210768933366526384796279', 'a10': [11.774403495228857, 0.0], 'a2': [2.3548806990457716, 0.0], 'a3': [-1.2059115431608491, 0.0], 'a4': [-2.4545368932616993, 0.0], 'a5': [5.0, 0.0], 'a6': [-2.8397778177459854, 0.0], 'a7': [20.760680611474168, 0.0], 'a8': [-24.619187147403917, 0.0], 'a9': [-25.54577735007142, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 61.65699595599897, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-5.0, 0]]], [11, [[1.0, 0], [-11.0, 0]]], [19, [[1.0, 0], [19.0, 0]]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.1', 'coefficient_field': 'CDF', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.3548806990457716, 0], [8.0, 0]], [[1.0, 0], [1.2059115431608491, 0], [27.0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [-20.760680611474168, 0], [343.0, 0]], [[1.0, 0], [-11.0, 0]], [[1.0, 0], [64.12988240704907, 0], [2197.0, 0]], [[1.0, 0], [-41.01671958323478, 0], [4913.0, 0]], [[1.0, 0], [19.0, 0]], [[1.0, 0], [-122.4331885016879, 0], [12167.0, 0]], [[1.0, 0], [-194.84032280718006, 0], [24389.0, 0]], [[1.0, 0], [-41.0170943546355, 0], [29791.0, 0]], [[1.0, 0], [-179.5345404490984, 0], [50653.0, 0]], [[1.0, 0], [57.135249147385196, 0], [68921.0, 0]], [[1.0, 0], [149.79885033398554, 0], [79507.0, 0]], [[1.0, 0], [81.0743204052541, 0], [103823.0, 0]], [[1.0, 0], [47.446207249197386, 0], [148877.0, 0]], [[1.0, 0], [-338.4870655577238, 0], [205379.0, 0]], [[1.0, 0], [-345.49637022995523, 0], [226981.0, 0]], [[1.0, 0], [-412.73960915327046, 0], [300763.0, 0]], [[1.0, 0], [1084.7243906858516, 0], [357911.0, 0]], [[1.0, 0], [-98.33092427906773, 0], [389017.0, 0]], [[1.0, 0], [-1183.7518447832006, 0], [493039.0, 0]], [[1.0, 0], [-672.4391326423383, 0], [571787.0, 0]], [[1.0, 0], [-187.30132374458285, 0], [704969.0, 0]], [[1.0, 0], [-544.9513457388573, 0], [912673.0, 0]], [[1.0, 0], [-1234.9141692422556, 0], [1030301.0, 0]], [[1.0, 0], [-1817.359857602094, 0], [1092727.0, 0]], [[1.0, 0], [1963.0680551193445, 0], [1225043.0, 0]], [[1.0, 0], [-320.78217495560426, 0], [1295029.0, 0]], [[1.0, 0], [-539.687995761526, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 59, 'label': '2-1045-1.1-c3-0-59', 'leading_term': '2.61395613594521370274778569033', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1045/4/a/e/1/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.6139561359452137, 2.5959535706382684, 2.5421291866215374, 2.4530334360999895, 2.3295853331403924, 2.173074402774595, 1.98516254888682, 1.7678850305502212, 1.5236495744604908, 1.2552325367819177, 0.9657709671469616, 0.6587494246067394, 0.337980451660203, 0.007577727577166437, -0.32807890646470883, -0.6643871347681561, -0.9965748824203341, -1.319762066624616, -1.6290310553060967, -1.9195051476159695, -2.1864340253381926, -2.4252847610808295, -2.63183662057323, -2.802277574786912, -2.9333001554331153, -3.0221940569271526, -3.0669327208517254, -3.066251046057296, -3.019711358207936, -2.9277548544264147, -2.7917359171006613, -2.6139369686376703, -2.3975619157349097, -2.1467067040102887, -1.8663060644748708, -1.5620561715719838, -1.2403136339105116, -0.9079719854447007, -0.5723176155332163, -0.24086784710752682, 0.07880538302013124, 0.37926209642106434, 0.6533863429834915, 0.8945785133106722, 1.0969422735678134, 1.2554602970061983, 1.3661529395317766, 1.4262141737466525, 1.4341194660967076, 1.3897008576588386, 1.2941852858987224, 1.1501931498228473, 0.9616952537447883, 0.7339275369168754, 0.4732643716360618, 0.18705264854059897, -0.1165896834660589, -0.4290055461706969, -0.7412547386952928, -1.0443864654694162, -1.3297198670087411, -1.5891233253950814, -1.8152829027067272, -2.0019501878868855, -2.14416010015717, -2.2384098373458206, -2.2827911640266967, -2.2770695911735737, -2.222705675116582, -2.1228156130775506, -1.9820704755396088, -1.8065357196589973, -1.6034549898427901, -1.3809845406897698, -1.147886818357803, -0.9131937128235619, -0.6858516522691672, -0.4743619660163237, -0.28643071942828596, -0.1286424636870672, -0.00617200482903078, 0.07745263879936012, 0.12052444805049782, 0.12325922792637808, 0.08781808156848998, 0.018246582556124172, -0.07966997349586612, -0.19863233172103267, -0.33012757012351057, -0.4647939546892597, -0.5928371626979811, -0.704481857374829, -0.7904403259454216, -0.8423783018627297, -0.853357286684587, -0.8182327453362478, -0.7339885139355946, -0.599989637729525, -0.418138613300702, -0.19292356810263325, 0.06864884464187161, 0.35723828013738484, 0.6614705857984831, 0.9683447966497412, 1.2637341410757637, 1.532963125315032, 1.7614385031732362, 1.9353084660576036, 2.0421219053643926, 2.0714582673576256, 2.0154984584371474, 1.8695085322367204, 1.6322105071522786, 1.3060185696924769, 0.8971239988738049, 0.4154182226850403, -0.1257497429781594, -0.709977899227662, -1.318366848255905, -1.9302079727181078, -2.5237790273198106, -3.0772160205486094, -3.569425501936247, -3.980998059589142, -4.295082193667889, -4.498177914617952, -4.5808114911438915, -4.538056726111726, -4.369873862364122, -4.0812445189984485, -3.6820896520100166, -3.18696706693549, -2.6145550702556073, -1.9869389727618474, -1.3287268711733968, -0.6660299532601366, -0.02535003938002618, 0.567577220458001, 1.0889314709491404, 1.5178958242058553, 1.8376320580503205, 2.036094597025132, 2.1066412489026005, 2.04840710333089, 1.866418316131112, 1.5714342618780883, 1.1795192103915306, 0.7113576768630981, 0.19134028080107493, -0.3535413105030433, -0.8949415935367421, -1.4044937591796987, -1.855165205853039, -2.2225711243399426, -2.486181809844043, -2.630363126272551, -2.6451964215049544, -2.5270339106562854, -2.2787576939442076, -1.9097246066632767, -1.4353943480320912, -0.8766540583687733, -0.2588679194590322, 0.38930535545261447, 1.0372718587288854, 1.6539735109603455, 2.2093988970299128, 2.6760588607239844, 3.030352413056172, 3.2537529641474316, 3.3337530380767384, 3.2645171257540895, 3.0472066378618314, 2.6899573413568114, 2.2075073730396153, 1.6204920086323666, 0.9544388714711162, 0.23851324736675597, -0.4959232506096075, -1.216867022110408, -1.8932595669254708, -2.4965246598284363, -3.00197495771594, -3.3900137566102524, -3.6470680759607825, -3.766203283154036, -3.7473863632546536, -3.5973837970556564, -3.3292998183890945, -2.9617804923356963, -2.5179274915035315, -2.0239816009667435, -1.507848918373498, -0.9975516658935706, -0.519689941226276, -0.09800030235733817, 0.24790822563350648, 0.5035700647344499, 0.6603742989350898, 0.7159319470826981, 0.6740797984919514, 0.5445223115796397, 0.3421341072416458, 0.08596542497329875, -0.2019896272988176, -0.49818816338855554, -0.7790133406653469, -1.02224047818102, -1.2084064605292377, -1.3220001195172784, -1.3524019750634124, -1.2945167962084025, -1.149061041824486, -0.9224882614809536, -0.6265577199160255, -0.27757350495882627, 0.10465816744976857, 0.4980881060593588, 0.8798207238891489, 1.2275601669793392, 1.5210147126917615, 1.7431704738692797, 1.8813533976947954, 1.9280116998352623, 1.8811684530926454, 1.7445149907224986, 1.5271387930176321, 1.242903154644458, 0.9095186696021466, 0.5473669429361953, 0.17815359348256996, -0.17652058324549166, -0.49657530753515994, -0.7647584379549313, -0.9677569245277874, -1.0970347719469478, -1.14933921438756, -1.1268380032221212, -1.036875225266928, -0.8913588286791162, -0.7058183488933575, -0.4981945048354529, -0.28744178825543487, -0.09203952090312673, 0.0714849620931961, 0.18991601072444045, 0.25449300698944455, 0.2617507525540442, 0.21398909538319272, 0.11932786324639048, -0.008669375588707022, -0.15178992588333987, -0.28834297302833667, -0.39463788421613366, -0.44667752006871436, -0.42195668996145413, -0.3012452291404962], 'positive_zeros': ['0.76304875380864664611197449970937', '2.32902698386702909885720800765866', '3.25904306175143552767256704946680', '4.69103473681941461138630542218360', '4.99265192576979071220733061635757', '5.84465691047977424850792843386144', '6.78373308357984944680666363875646', '7.971145792297742194571809130702693', '8.692600830553736618802917294595785', '9.515766077986292970691417948312088'], 'prelabel': '2-1045-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.85219688724111, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76304875380864664611197449971', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.32902698386702909885720800766', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.25904306175143552767256704947', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 61.65699595599897, 'bad_primes': [5, 11, 19], 'central_character': '1.1', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 2, 'index': 59, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1045/4/a/e/1/14'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-1045-1.1-c3-0-59', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1045-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.85219688724111, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76304875380864664611197449971', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '967279210768933366526384796279', 'Lhash_array': ['967279210768933366526384796279'], 'label': '2-1045-1.1-c3-0-59', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1045/4/a/e/1/14'}